<h2>题目编号 : 109</h2>
<div style="color:#666;font-size:80%;">18 November 2005</div><br />
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<p>In the game of darts a player throws three darts at a target board which is split into twenty equal sized sections numbered one to twenty.</p>
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<img src='project/images/p_109.gif' width='400' height='400' alt='' /><br />
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<p>The score of a dart is determined by the number of the region that the dart lands in. A dart landing outside the red/green outer ring scores zero. The black and cream regions inside this ring represent single scores. However, the red/green outer ring and middle ring score double and treble scores respectively.</p>
<p>At the centre of the board are two concentric circles called the bull region, or bulls-eye. The outer bull is worth 25 points and the inner bull is a double, worth 50 points.</p>
<p>There are many variations of rules but in the most popular game the players will begin with a score 301 or 501 and the first player to reduce their running total to zero is a winner. However, it is normal to play a &quot;doubles out&quot; system, which means that the player must land a double (including the double bulls-eye at the centre of the board) on their final dart to win; any other dart that would reduce their running total to one or lower means the score for that set of three darts is &quot;bust&quot;.</p>
<p>When a player is able to finish  on their current score it is called a &quot;checkout&quot; and the highest checkout is 170: T20 T20 D25 (two treble 20s and double bull).</p>
<p>There are exactly eleven distinct ways to checkout on a score of 6:</p>
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<table border='1' cellpadding='3' cellspacing='0' align='center'>
<tr>
<td><img src='images/spacer.gif' width='80' height='1' alt='' /><br />D3</td>
<td><img src='images/spacer.gif' width='80' height='1' alt='' /><br />&nbsp;</td>
<td><img src='images/spacer.gif' width='80' height='1' alt='' /><br />&nbsp;</td>
</tr>
<tr>
<td>D1</td>
<td>D2</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>S2</td>
<td>D2</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>D2</td>
<td>D1</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>S4</td>
<td>D1</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>S1</td>
<td>S1</td>
<td>D2</td>
</tr>
<tr>
<td>S1</td>
<td>T1</td>
<td>D1</td>
</tr>
<tr>
<td>S1</td>
<td>S3</td>
<td>D1</td>
</tr>
<tr>
<td>D1</td>
<td>D1</td>
<td>D1</td>
</tr>
<tr>
<td>D1</td>
<td>S2</td>
<td>D1</td>
</tr>
<tr>
<td>S2</td>
<td>S2</td>
<td>D1</td>
</tr>
</table>
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<p>Note that D1 D2 is considered <b>different</b> to D2 D1 as they finish on different doubles. However, the combination S1 T1 D1 is considered the <b>same</b> as T1 S1 D1.</p>
<p>In addition we shall not include misses in considering combinations; for example, D3 is the <b>same</b> as 0 D3 and 0 0 D3.</p>
<p>Incredibly there are 42336 distinct ways of checking out in total.</p>
<p>How many distinct ways can a player checkout with a score less than 100?</p>

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